Image forming apparatus and image forming system

ABSTRACT

An image forming apparatus comprises an image data generating unit configured to convert a tone of an input value which indicates a density of a pixel by using a predetermined dither matrix and generate image data. The image forming apparatus further comprises a drive source and a gear configured to transmit a drive force from the drive source to an image carrier. The dither matrix includes a plurality of sub-matrixes arranged in a predetermined rule and a dot in each of the plurality of the sub-matrixes grows from a corresponding original point. The image forming apparatus satisfies a relation of (1) a≧0.24 mm and b/a&lt;0.78, or (2) a&lt;0.24 mm and b/a&gt;1.2, where “a” is a travel distance of a printing medium per tooth of the gear in a secondary scanning direction orthogonal to the primary scanning direction, and “b” is a component in the secondary scanning direction of a distance between the original point of the dot derived from a first sub-matrix and the original point of the dot derived from a second sub-matrix.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Japanese PatentApplication No. 2008-223181, filed Sep. 1, 2008, the entire subjectmatter and disclosure of which is incorporated herein by reference.

BACKGROUND

1. Technical Field

The present invention relates to an image forming apparatus and an imageforming system which performs halftoning by using a dither matrix.

2. Description of the Related Art

In a known image forming apparatus of an electrophotographic type, anelectrically charged photoconductor drum is irradiated with a lightsource such as a laser and the voltage of a corresponding portion of thephotoconductor drum is changed to cause toner to adhere thereto. Then, atoner image formed on the photoconductor drum is transferred to aprinting paper by a transfer roller applied with a voltage opposite fromthe photoconductor drum. Thereafter, a fixing roller fixes the tonerwith heat and pressure. Accordingly, a printing result is obtained onthe printing paper.

Here, in order to express tones of an image artificially, there is acase such that a halftoning using a dither matrix is performed. By thehalftoning, for example, input image data of 256 tones is converted intotwo-tone output image data, and an image is formed on the basis of theoutput image data, so that dots of a size according to the tone arearranged discretely at regular pitches, whereby an image in which thetone is artificially reproduced is formed.

However, when the photoconductor drum is driven by a drum gear, a driveforce from a drive motor is transmitted to the photoconductor drum via adrive gear and the above-described drum gear engaging therewith. In thisconfiguration, when the drive gear and the drum gear engage, the unevenrotation occurs. It may causes that the pitches of the dots discretelyarranged and the cycle of uneven rotation get closer as a result of thehalftoning, interference may occur between them, and inconsistencies indensity may be generated.

SUMMARY

A need has arisen to provide an image forming apparatus and an imageforming system in which generation of inconsistencies in density in aprinting medium may be reduced or restrained.

According an embodiment of the present invention, an image formingapparatus comprises an image data generating unit configured to converta tone of an input value which indicates a density of a pixel by using apredetermined dither matrix and generate image data. The image formingapparatus further comprises a scanning unit configured to scan an imagecarrier in a primary scanning direction according to the image datagenerated by the image data generating unit and an image forming unitconfigured to form, on a printing medium, an image corresponding to theimage data scanned by the scanning unit. The image forming apparatusstill further comprises a drive source and a gear configured to transmita drive force from the drive source to the image carrier. The dithermatrix includes a plurality of sub-matrixes arranged in a predeterminedrule and each of the plurality of sub-matrix having predeterminedthreshold values such that a dot in each of the plurality of thesub-matrixes grows from a corresponding original point. The plurality ofsub-matrixes includes a first sub-matrix and a second sub-matrix whichhas a predetermined positional relation with the first sub-matrix. Theimage forming apparatus satisfies a relation of (1) a≧0.24 mm andb/a<0.78, or (2) a<0.24 mm and b/a>1.2, where “a” is a travel distanceof a printing medium per tooth of the gear in a secondary scanningdirection orthogonal to the primary scanning direction, and “b” is acomponent in the secondary scanning direction of a distance between theoriginal point of the dot derived from the first sub-matrix and theoriginal point of the dot derived from the second sub-matrix.

According an embodiment of the present invention, an image formingsystem comprises an image forming apparatus and a computer whichcommunicate with the image forming apparatus. The image formingapparatus comprises a scanning unit configured to scan an image carrierin a primary scanning direction according to image data and an imageforming unit configured to form, on a printing medium, an imagecorresponding to the image data scanned by the scanning unit. The imageforming apparatus further comprises a drive source and a gear configuredto transmit a drive force from the drive source to the image carrier.The computer comprises an image data generating unit configured toconvert an input value which indicates a density of a pixel by using apredetermined dither matrix and generate image data. The dither matrixincludes a plurality of sub-matrixes arranged in a predetermined ruleand each of the plurality of sub-matrix having predetermined thresholdvalues such that a dot in each of the plurality of the sub-matrixesgrows from a corresponding original point. The plurality of sub-matrixesincludes a first sub-matrix and a second sub-matrix which has apredetermined positional relation with the first sub-matrix. The imageforming system satisfies a relation of (1) a≧0.24 mm and b/a<0.78, or(2) a<0.24 mm and b/a>1.2, where “a” is a travel distance of a printingmedium per tooth of the gear in a secondary scanning directionorthogonal to the primary scanning direction, and “b” is a component inthe secondary scanning direction of a distance between the originalpoint of the dot derived from the first sub-matrix and the originalpoint of the dot derived from the second sub-matrix.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention, the needssatisfied thereby, and the features and advantages thereof, referencenow is made to the following descriptions taken in connection with theaccompanying drawings.

FIG. 1 is a schematic cross-sectional view of a laser printer as anembodiment of an image forming apparatus.

FIG. 2 is a schematic drawing showing a drum driving mechanism.

FIG. 3 is a block diagram showing an electric configuration of the laserprinter.

FIG. 4 is a drawing showing an example of a dither matrix.

FIG. 5A is a conceptual drawing showing a relation between originalpoints of dots arranged regularly on a printing paper and ranges thatsub-matrixes cover.

FIG. 5B is a drawing showing arrows passing through the original pointsof the dots formed on the printing paper in parallel to a primaryscanning direction being overlapped with the conceptual drawing shown inFIG. 5A.

FIG. 5C is a drawing showing displacement of the positions of formationof the original points of the dots due to the deviation of transport.

FIG. 6A is a drawing showing a relation between a sub-matrix having 3×3elements and a basic unit formed as an assembly of the sub-matrixes.

FIG. 6B is a conceptual drawing showing a range that a dither matrix inPattern 1 formed by combining the basic units as shown in FIG. 6Acovers.

FIG. 7A is a drawing showing a relation between a sub-matrix having 3×3elements and a basic unit formed as an assembly of the sub-matrixes.

FIG. 7B is a conceptual drawing showing a range that a dither matrix inPattern 2 formed by combining the basic units as shown in FIG. 7Acovers.

FIG. 8A is a drawing showing a relation between a sub-matrix having 4×4elements and a basic unit formed as an assembly of the sub-matrixes.

FIG. 8B is a conceptual drawing showing a range that a dither matrix inPattern 3 formed by combining the basic units as shown in FIG. 8Acovers.

FIG. 9A is a drawing showing a relation between a sub-matrix having 4×4elements and a basic unit formed as an assembly of the sub-matrixes.

FIG. 9B is a conceptual drawing showing a range that a dither matrix inPattern 4 formed by combining the basic units as shown in FIG. 9Acovers.

FIG. 10 is a conceptual drawing showing a dither matrix in Pattern 5formed by combining the sub-matrixes including 3×3 elements, and a rangethat the dither matrix covers.

FIG. 11 is a conceptual drawing showing a dither matrix in Pattern 6formed by combining the sub-matrixes including 4×4 elements, and a rangethat the dither matrix covers.

FIG. 12A is a conceptual drawing showing a range that a dither matrix inPattern 7 covers.

FIG. 12B is a conceptual drawing showing a range that a dither matrix inPattern 8 covers.

FIG. 13 is a drawing showing a result of experiment which has inspectedan adequate range of a gear pitch a for respective line pitches b whenthe dither matrixes from Pattern 1 to Pattern 8 described with referenceto FIG. 6 to FIG. 12B are applied.

FIG. 14A is a drawing showing a basic unit configured as an assembly ofthe sub-matrixes having 4×4 elements.

FIG. 14B is a drawing for explaining a relation between an arrangementof the sub-matrixes, a screen angle, and the number of screen lines.

FIG. 14C is a drawing for explaining the relation between thearrangement of the sub-matrixes, the screen angle, and the number ofscreen lines.

FIG. 15A is a drawing showing a relation between the arrangement of thesub-matrixes and a screen angle θ.

FIG. 15B is a drawing showing the relation between the arrangement ofthe sub-matrixes and the screen angle θ.

FIG. 15C is a drawing showing the relation between the arrangement ofthe sub-matrixes and the screen angle θ.

FIG. 16A is a drawing showing a relation between the basic unit and thedither matrix configured as an assembly of the basic unit.

FIG. 16B is a drawing showing an example of smallest threshold values tobe allocated to the respective sub-matrixes.

FIG. 17 is a drawing for explaining a method of determining the size ofa large dither.

FIG. 18A is a drawing showing an example of a sequence of growth of thedot for forming a rod-like dot parallel to the primary scanningdirection.

FIG. 18B is a drawing showing an example of the threshold valuesallocated to the dither matrix according to the smallest threshold valueshown in FIG. 16B and the sequence of the growth of the dot shown inFIG. 18A.

FIG. 19A is a drawing explaining an example of adjustment of thethreshold values arranged in the dither matrix.

FIG. 19B is a drawing explaining an example of the adjustment of thethreshold values arranged in the dither matrix.

FIG. 20 is a block diagram showing an electric configuration between aPC and a laser printer connected to the PC so as to allow thecommunication therewith.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the present invention and their features and advantagesmay be understood by referring to FIGS. 1-20, like numerals being usedfor like corresponding parts in the various drawings.

FIG. 1 is a schematic cross-sectional view of a laser printer 1 as anembodiment of an image forming apparatus. As shown in FIG. 1, the laserprinter 1 comprises a printer casing 4 comprising an upper casing 2 anda lower casing 3, a laser scanner apparatus 5 provided on the uppercasing 2, a process cartridge 6 demountably provided on the lower casing3, a transferring and separating device 9 comprising a transfer charger7 and a charge removing needle 8, a fixing device 12 comprising a heatroller 10 and a pressure roller 11, and a transporting apparatus 17comprising a paper feeding roller 13, a resist roller 14, a transferroller 36 configured to transfer a visible image on a photoconductordrum 28 to a printing paper 33, a transporting roller 15, and apaper-discharging roller 16.

The laser scanner apparatus 5 comprises a semiconductor laser 22, ahexahedron mirror 23, an imaging lens 24, a reflecting mirror 25, and alens member 27 formed of synthetic resin provided at a laser lightoutlet portion 26. The process cartridge 6 is demountably disposed inthe lower casing 3, and comprises the photoconductor drum 28 and adeveloping cylinder 30 integrally assembled in the interior thereof.

A laser light 35 emitted from the semiconductor laser 22 and enteredinto the hexahedron mirror 23 is deflected by a predetermined angle viaevery mirror surfaces of the hexahedron mirror 23 rotating at a constanthigh speed for primary scanning over a predetermined angular range, ispassed through the imaging lens 24, is reflected vertically downward bythe reflecting mirror 25, then is passed through the lens member 27elongated in a scanning direction of the laser light 35, and enters thephotoconductor drum 28. The laser light 35 entered into thephotoconductor drum 28 performs a secondary scanning with thephotoconductor drum 28 rotating at a constant velocity by a drum drivingmechanism 40 (shown in FIG. 2) described later, so that an electrostaticlatent image is formed on a peripheral surface of the photoconductordrum 28. The laser printer 1 scans the photoconductor drum 28 accordingto image data described later to form an electrostatic latent imageaccording to the image data.

The electrostatic latent image formed on the photoconductor drum 28 isdeveloped by toner supplied from the developing cylinder 30 and istransferred onto the printing paper 33, then the printing paper 33 isseparated from the photoconductor drum 28 by the charge removing needle8 and is transported to the fixing device 12. The fixing device 12 isconfigured to fuse and fix the toner to the printing paper 33 by theheat roller 10 and the pressure roller 11, and then transport theprinting paper 33 onto a paper discharging tray 34 via the transportingroller 15 and the paper-discharging roller 16.

FIG. 2 is a schematic drawing showing the drum driving mechanism 40. Alarge-diameter drum gear 41 formed of synthetic resin is secured to adrum shaft 28 a of the photoconductor drum 28, and a small-diameter drumdriving gear 42 which engages the drum gear 41 is driven to rotate by acoupling mechanism coupled to a main motor M as a drive source. In otherwords, the drum driving mechanism 40 comprises gears 41, 42 configuredto transmit a drive force from the main motor M to the photoconductordrum 28. In contrast, the paper feeding roller 13, the resist roller 14,the transfer roller 36, the transporting roller 15, thepaper-discharging roller 16, and the like described with reference toFIG. 1 are configured to be driven to rotate by the main motor Msynchronously with the velocity of rotation of the photoconductor drum28. In other words, the printing paper 33 is configured to betransported synchronously with the rotation of the photoconductor drum28.

Here, in a case where the drum gear 41, that is, the photoconductor drum28 is driven to rotate by the rotation of the drum driving gear 42,since it is achieved by engagement between gear teeth 42 a of the drumdriving gear 42 and gear teeth 41 a of the drum gear 41, an engagingoperation from a start-of-engagement phase angle to an end-of-engagementphase angle of the gear tooth 42 a with respect to the gear tooth 41 ais repeated at every tooth 41 a of the drum gear 41 and, consequently,the velocity of rotation of the drum gear 41, that is, of thephotoconductor drum 28 changes every pitch angle α between the adjacenttwo gear teeth 41 a depending on accuracy of finishing or material ofthe drum gear 41.

When the drum gear 41 is rotated by the pitch angle α, that is, by acircular pitch (obtained by dividing a pitch circle by the number ofteeth) a travel distance by which a point on a surface of thephotoconductor drum 28 is moved is defined as a gear pitch “a”. Thevalue of the gear pitch “a” is obtained by a unit of mm. Since thephotoconductor drum 28 is subjected to unevenness of the velocity ofrotation when the gear tooth 41 a engages the gear tooth 42 a,inconsistencies in density occur on a printing result on the printingpaper 33 every gear pitch a due to the unevenness of the velocity.

FIG. 3 is a block diagram showing an electric configuration of the laserprinter 1. As shown in FIG. 3, a video controller 50 of the laserprinter 1 comprises a CPU 51, a ROM 52 in which various control programsstored therein, a RAM 53 provided with various memories such asreceiving buffers configured to receive and store image data transmittedfrom a data transmitting instrument (not shown) such as a personalcomputer or a host computer, a serial interface (S.I/F) 54 configured toreceive data transmitted from the external data transmitting instrument(not shown), and a video interface (V.I/F) 55 configured to output printdata converted into bit image data in sequence to a DC controller 58,and these members are connected respectively to the CPU 51.

Here, a printing mechanism PM is provided with the above-described laserscanner apparatus 5, the process cartridge 6, the transferring andseparating device 9, the fixing device 12, and the transportingapparatus 17, as well as the main motor M which drives thephotoconductor drum 28 and the transporting apparatus 17, a fixingheater for the heat roller 10, and other electrical component circuits,and the DC controller 58 is configured to control the drive of a scannermotor which drives the semiconductor laser 22 and the hexahedron mirror23 in addition to the main motor M, the fixing heater, and variouselectric component circuits.

The ROM 52 stores a preset dither matrix 52 a in addition to the variouscontrol programs provided in normal laser printers. The CPU 51 functionsas image data generating unit configured to generate image data byperforming a halftoning according to the control programs stored in theROM 52.

In the halftoning, the dither matrix 52 a is superimposed on an inputimage, and input values which represent densities of pixels of the inputimage are compared with threshold values, which are elementsconstituting the dither matrix 52 a, in one-to-one correspondence. Then,when the input value is equal to or larger than the threshold value, theinput value is converted into “1” which means that the toner is fixed tothe pixels having the corresponding input value, and if the input valueis smaller than the threshold value, the input value is converted into“0” which means that the toner is not fixed to the pixels having thecorresponding input value, so that the input values of the 256 tones areconverted into two-tone image data. Therefore, the larger the number ofpixels having the input values equal to or larger than the thresholdvalue in the pixels within a range that the dither matrix 52 a covers,the more the pixels on which the toner is to be fixed within thecorresponding range increases, so that the tones of the image can beartificially expressed. Here, the CPU 51 corrects and outputs the imagedata by a known image processing such as gamma correction or the liketogether with the halftoning.

FIG. 4 is a drawing showing an example of the dither matrix 52 a storedin the ROM 52 of the laser printer 1. In the halftoning, the dithermatrix 52 a is superimposed on the input image in a positionalrelationship such that a lateral direction of the dither matrix 52 ashown in FIG. 4 corresponds to a primary scanning direction, and avertical direction of the dither matrix 52 a corresponds to a secondaryscanning direction, so that the threshold values and the input values ofthe pixels are compared.

As shown in FIG. 4, the dither matrix 52 a includes sets of sixteensub-matrixes 60 arranged regularly.

In each of the sub-matrixes 60, a smallest threshold value within thesub-matrix 60 (hereinafter, referred simply as smallest threshold value)is arranged at a left end of an uppermost row. Then, in the uppermostrow, a row of threshold values arranged in an ascending order from theleft end to a right end is allocated. In a second uppermost row, a rowof threshold values arranged in the ascending order from a thresholdvalue which is next largest after the rightmost threshold value of theuppermost row is allocated. In this manner, the threshold values arearranged in sequence so as to be larger as it goes toward the lowerrows.

In other words, the sub-matrix 60 includes the threshold values set insuch a manner that one dot formed at an original point which correspondsto the smallest threshold value extends in the primary scanningdirection as the density of the pixel within a range that the sub-matrix60 covers increases to form a rod-like dot shape, and the rod-like dotis increased in thickness in the secondary scanning direction as thedensity further increases.

Subsequently, arrangement of the sub-matrixes 60 which constitute thedither matrix 52 a will be described. As shown in FIG. 4, in the dithermatrix 52 a, the sub-matrixes 60 adjacent to each other in the lateraldirection (corresponding to the primary scanning direction) are arrangedregularly by being shifted by one threshold value in the verticaldirection (corresponding to the secondary scanning direction). Since onedot is formed corresponding to one sub-matrix 60 as described above,according to the dither matrix 52 a, the respective dots correspondingto the sub-matrixes 60 are formed in regular arrangement so that theoriginal points are shifted in the secondary scanning direction by anextent corresponding to one pixel.

FIG. 5A is a conceptual drawing showing a relation between originalpoints 61 of the dots arranged regularly on the printing paper 33, andranges 52 b that the dither matrixes 52 a cover. As described withreference to FIG. 4, sixteen sub-matrixes are included in one dithermatrix 52 a, and hence sixteen original points 61 at maximum are formeddiscretely in the range 52 b that the one dither matrix 52 a covers asshown in FIG. 5A. When the density of the pixel within the range thatthe dither matrix 52 a covers is small, that is, in a low-densityportion, the dots each extends from the original point 61 in the primaryscanning direction into a rod-like dot shape. In other words, therod-like dots grow in a direction of arrows shown in FIG. 5B.

There is a case where positions of formation of the dots are shifted inthe secondary scanning direction thereby causing uneven dot density dueto deviation of transport caused by tolerances of the various components(a displacement caused by variations in the gear pitch a), and hencecyclic inconsistencies in density show up on the printing paper 33.Then, even through such inconsistencies in density are little andinconspicuous, the inconsistencies in density are emphasized due to theinterference depending on the relation between the cycle of occurrenceof the inconsistencies in density and the distance between the originalpoints 61 described above, so that the image quality might be remarkablylowered. The present inventor focused attention on a relationship amongthe inconsistencies in density triggered by the deviation of transportcaused by the variations in the gear pitch a, the distance between theoriginal points 61 having a positional relationship which is liable tocause the emphasis of the inconsistencies in density, and the gear pitcha.

Referring now to FIG. 5C, the positional relationship which is liable totrigger the inconsistencies in density caused by the deviation oftransport will be described. FIG. 5C is a drawing showing displacementof the positions of formation of the original points of the dots due tothe deviation of transport.

Assuming that there is no deviation of transport of the printing paper33, the original point of the dot which is to be formed at a position P2shown in FIG. 5C is actually formed at a position P2′ shifted by anamount σ in the secondary scanning direction by being influenced by thedeviation of transport. The sign σ represents the deviation oftransport, that is, an estimated amount of displacement caused by thevariations in the gear pitch a. The value of σ can be estimated from thetolerances of the respective components.

When a distance A between a P1 and the P2 is changed to a distance Bbetween the P1 and P2′ due to the deviation of transport, the amount ofchange causes a change in density per unit area, so that theinconsistencies in density are brought into visual perception.

The present inventor has found that the density change is calculated inthe following manner in order to verify an extent of the change indensity generated among the dots. First of all, an estimated value ofthe distance A between the P1 and P2 is calculated using the followingexpression (1). In the expression, a component in the primary scanningdirection of the distance A is expressed by X, and a component in thesecondary scanning direction is expressed by Y.

A=√{square root over (X² +Y ²)}  (1)

Subsequently, an estimated value of the distance B between the P1 andP2′ is calculated using the following expression (2).

B=√{square root over (X²+(Y+σ)²)}  (2)

The ratio of the change of the distances A and B between the two pointsis visually perceptible as the inconsistencies in density. Therefore,the density change is defined as the expression (3).

$\begin{matrix}{{{density}\mspace{14mu} {change}} = {{B/A} = \sqrt{1 + \frac{\sigma^{2} + {2y\; \sigma}}{X^{2} + Y^{2}}}}} & (3)\end{matrix}$

In other words, it is understood that the smaller the distance betweenthe two points and the larger the value of Y (the component in thesecondary scanning direction of the distance between the two points),the larger the density change becomes and the higher the probability ofoccurrence of the inconsistencies in density becomes. The presentinventor focused attention on the positional relationship of theoriginal points of the dots which maximize the density change.

More specifically, a first sub-matrix and a second sub-matrix which hasa predetermined positional relationship determined on the basis of theabove described density change are determined from the plurality ofsub-matrixes 60 (see FIG. 4) which constitute the dither matrix 52 a. Inother words, the first sub-matrix and the second sub-matrix aredetermined so that the density change between the original point 61 ofthe dot derived from the first sub-matrix and the original point 61 ofthe dot derived from the second sub-matrix is maximized. Then, thecomponent in the secondary scanning direction of a distance between theoriginal point 61 of the dot derived from the first sub-matrix and theoriginal point 61 of the dot derived from the second sub-matrix isexpressed as a line pitch b (see FIG. 5B), and the laser printer 1 inthis embodiment is configured in such a manner that a relationshipbetween the line pitch b and the gear pitch a satisfies a relationalexpression a≧0.24 mm and b/a<0.78 or a<0.24 mm and b/a>1.2. In thismanner, the occurrence of the inconsistencies in density can berestrained adequately. The value of the line pitch b is obtained in aunit of mm.

By determining the first sub-matrix and the second sub-matrix using thedensity change described above, the component in the secondary scanningdirection of the distance between the dots having the relationship whichis liable to cause the inconsistencies in density, that is, therelationship such that the distance between the original points of thedots is small and the component in the secondary scanning direction ofthe corresponding distance is large can be set to be the line pitch b,so that the inconsistencies in density can be reduced or restrainedadequately.

Also, in a case of employing a dither matrix having a configurationdifferent from the dither matrix 52 a described with reference to FIG. 4and FIGS. 5A and 5B, the effect of restraining the interference fringesis also achieved by applying the numerical value range described above.

Referring now to FIGS. 6A and 6B to FIG. 13, various dither matrixeshaving configurations different from the dither matrix 52 a areexemplified, and the effect obtained when the numerical value rangedescribed above is applied about the various dither matrixes shown inFIGS. 6A and 6B to FIG. 13 will be described.

FIG. 6A is a drawing showing a relation between a sub-matrix 64 having3×3 elements and a basic unit 66 formed by assembling four sub-matrixes64. As shown in FIG. 6A, by configuring the basic unit 66 by shiftingthe sub-matrixes 64 having 3×3 elements by an extent corresponding tothree elements in the primary scanning direction and by an extentcorresponding to one element in the secondary scanning direction, anangle of a line connecting the original points of the dots formed withrespect to the primary scanning direction (hereinafter, referred to as ascreen angle θ) becomes about 18°.

A threshold value which does not belong to any sub-matrix 64, which issurrounded by the sub-matrixes 64, is referred to as an inter-sub-matrixcell C, hereinafter. As shown in FIG. 6A, the basic unit 66 isconfigured to include one inter-sub-matrix cell C.

FIG. 6B is a conceptual drawing showing a dither matrix formed bycombining the basic units 66 as shown in FIG. 6A (hereinafter referredto as Pattern 1), and a range that the dither matrix covers. Whenperforming the halftoning using the dither matrix in Pattern 1 at aresolution of 600 dpi, the number of screen lines is about 190 lpi (lineper inch), and the line pitch b has a length corresponding to fourpixels (about 0.169 mm). The term “the number of screen lines” means avalue which indicates the number of original points of the dots includedper inch in a direction vertical to a line L connecting the originalpoints of the dots.

FIG. 7A is a drawing showing a relation between the sub-matrix 64 having3×3 elements and a basic unit 68 formed by assembling four sub-matrixes64. As shown in FIG. 7A, with the basic unit 68 formed by shifting thesub-matrixes 64 having 3×3 elements by an extent corresponding to oneelement in the primary scanning direction and by an extent correspondingto three elements in the secondary scanning direction, the screen angleθ becomes about 72°. As shown in FIG. 7A, the basic unit 68 isconfigured to include one inter-sub-matrix cell C.

FIG. 7B is a conceptual drawing showing a range that a dither matrixformed by combining the basic units 68 as shown in FIG. 7A (hereinafterreferred to as Pattern 2) covers. When performing the halftoning usingthe dither matrix in Pattern 2 at the resolution of 600 dpi, the numberof screen lines is about 190 lpi, and the line pitch b has the lengthcorresponding to three pixels (about 0.127 mm).

FIG. 8A is a drawing showing a relation between the sub-matrix 60 having4×4 elements and a basic unit 70 formed by assembling four sub-matrixes60. As shown in FIG. 8A, with the basic unit 70 formed by shifting thesub-matrix 60 having 4×4 elements by an extent corresponding to fourelements in the primary scanning direction and by an extentcorresponding to one element in the secondary scanning direction, thescreen angle θ becomes about 14°. As shown in FIG. 8A, the basic unit 70is configured to include one inter-sub-matrix cell C.

FIG. 8B is a conceptual drawing showing a range that a dither matrixformed by combining the basic units 70 as shown in FIG. 8A (hereinafterreferred to as Pattern 3) covers. When performing the halftoning usingthe dither matrix in Pattern 3 at the resolution of 600 dpi, the numberof screen lines is about 145 lpi, and the line pitch b has the lengthcorresponding to five pixels (about 0.212 mm).

FIG. 9A is a drawing showing a relation between the sub-matrix 60 having4×4 elements and a basic unit 72 formed as an assembly of thesub-matrixes 60. As shown in FIG. 9, with the basic unit 72 formed byshifting the sub-matrix 60 having 4×4 elements by an extentcorresponding to one element in the primary scanning direction and by anextent corresponding to four elements in the secondary scanningdirection, an angle of the line connecting the original points of dotsformed with respect to the primary scanning direction becomes about 76°.The basic unit 72 is configured to include the inter-sub-matrix cell Cincluding two threshold values in total; two in the vertical direction,and one in the lateral direction.

FIG. 9B is a conceptual drawing showing a range that a dither matrixformed by combining the basic units 72 as shown in FIG. 9A (hereinafterreferred to as Pattern 4) covers. When performing the halftoning usingthe dither matrix in Pattern 4 at the resolution of 600 dpi, the numberof screen lines is about 137 lpi, and the line pitch b has a lengthcorresponding to four pixels (about 0.169 mm).

FIG. 10 is a conceptual drawing showing a dither matrix in Pattern 5formed by combining the sub-matrixes 64 including 3×3 elements, and arange that the dither matrix covers. The sub-matrixes 64 shown in FIG.10 are arranged with the intermediary of the inter-sub-matrix cell Cincluding two threshold values in total; two in the lateral directionand one in the vertical direction, between the four sub-matrixes 64.When performing halftoning using the dither matrix in Pattern 5 at theresolution of 600 dpi, the number of screen lines is about 172 lpi, andthe line pitch b has the length corresponding to four pixels (about0.169 mm). The screen angle is about 18.4°.

FIG. 11 is a conceptual drawing showing a dither matrix in Pattern 6formed by combining the sub-matrixes 60 including 4×4 elements, and arange that the dither matrix covers. The sub-matrixes 60 shown in FIG.11 are arranged with the intermediary of the inter-sub-matrix cell Cincluding two threshold values in total; two in the lateral directionand one in vertical direction, between the four sub-matrixes 60.According to the dither matrix in Pattern 6 as described above, thenumber of screen lines is about 137 lpi, and the line pitch b has thelength corresponding to five pixels (about 0.212 mm). The screen angleis about 14°.

FIG. 12A is a conceptual drawing showing a dither matrix in Pattern 7formed by combining the sub-matrixes 60 including 3×3 elements, and arange that the dither matrix covers. The sub-matrixes 60 shown in FIG.12A are arranged with the intermediary of the inter-sub-matrix cell Cincluding nine threshold values in total; three in the lateral directionand three in vertical direction, between the four sub-matrixes 60.According to the dither matrix in Pattern 7 as described above, thenumber of screen lines is about 141 lpi, and the line pitch b has thelength corresponding to six pixels (about 0.254 mm). The screen angle isabout 45°.

FIG. 12B is a conceptual drawing showing a dither matrix in Pattern 8formed by combining the sub-matrixes 65 including 5×5 elements, and arange that the dither matrix covers. The sub-matrixes 65 shown in FIG.12B are arranged with the intermediary of the inter-sub-matrix cell Cincluding one threshold value between the four sub-matrixes 60.According to the dither matrix in Pattern 8 as described above, thenumber of screen lines is about 118 lpi, and the line pitch b has thelength corresponding to six pixels (about 0.254 mm). The screen angle isabout 11°.

FIG. 13 is a drawing showing a result of experiment which has inspectedan adequate range of the gear pitch a for respective line pitches b whenthe dither matrixes from Pattern 1 to Pattern 8 described with referenceto FIGS. 6A and 6B to FIG. 12 are applied.

The present inventor has done an experiment about whether theinconsistencies in density were generated or not as a result of printingout the image data applied with the halftoning using the dither matrixesfrom Pattern 1 to Pattern 8 using a laser printer at the resolution of600 dpi. The number of teeth was changed by changing the outer diameterof the gear while fixing the module of the gear and the gear pitch a waschanged accordingly.

In a table shown in FIG. 13, “GOOD” indicates that no inconsistency indensity is generated or the inconsistencies in density are restrained toan allowable level, and “NG” indicates that the inconsistencies indensity are generated to an extent exceeding the allowable level.Numerical values (b/a) obtained by dividing the line pitch b by the gearpitch a are shown above “GOOD” or “NG” indicate the results ofevaluation.

As shown in FIG. 13, a result such that when the relational expression;a≧0.24 mm and b/a<0.78 is satisfied, no inconsistency in density isgenerated or the inconsistencies in density are restrained to theallowable level was obtained. Also, a result such that when therelational expression; a<0.24 mm and b/a>1.2 is satisfied, noinconsistency in density is generated or the inconsistencies in densityare restrained to the allowable level was obtained.

Subsequently, referring now to FIGS. 14A, 14B and 14C to FIGS. 19A, and19B, a sequence of designing the dither matrix will be described. Whendesigning the dither matrix, first of all, the size (the number ofelements) of the sub-matrixes is determined from the intended number ofscreen lines. For example, when a range of the number of screen linesfrom 150 lpi to 200 lpi is intended, a size of the sub-matrix of 3×3 isdetermined. Also, For example, when a range of the number of screenlines from 120 lpi to 150 lpi is intended, a size of the sub-matrix of4×4 is determined.

Subsequently, arrangement of the sub-matrixes which constitute the basicunit is determined from the intended screen angle and the number ofscreen lines.

FIG. 14A is a drawing showing a basic unit 62 including foursub-matrixes 60 each having 4×4 elements. With the arrangement ofsub-matrixes 60 as shown in FIG. 14A, the screen angle θ of about 14°,and the number of screen lines of about 145 lpi are achieved.

As a matter of course, the screen angle θ and the number of screen linescan be changed as needed by configuring the basic unit bydifferentiating the size or the arrangement of the sub-matrixes.

FIG. 14B shows an example in which the inter-sub-matrix cell C whichcorresponds to one element in the vertical direction is interposedbetween the sub-matrixes 64 of 3×3. In this case, the screen angle θalways becomes about 18°. Also, by increasing and decreasing the numberof elements in the inter-sub-matrix cell C in the lateral direction, thenumber of screen lines can be changed as needed.

In the same manner, FIG. 14C shows an example in which theinter-sub-matrix cell C which corresponds to one element in the lateraldirection is interposed between a pair of the sub-matrixes 64 of 3×3. Inthis case, the screen angle θ always becomes about 72°. Also, byincreasing and decreasing the number of elements in the inter-sub-matrixcell C in the vertical direction, the number of screen lines can bechanged as needed.

Referring now to FIGS. 15A, 15B and 15C, the relation between thearrangement of the sub-matrixes and the screen angle θ will further bedescribed. FIG. 15A is a drawing showing an example of arrangement ofthe sub-matrixes for forming a screen angle of about 34°. As shown inFIG. 15A, by arranging the inter-sub-matrix cell C which corresponds totwo elements in the vertical direction and one element in the lateraldirection so as to be interposed between the sub-matrixes 64 of 3×3, thescreen angle of about 34° is achieved.

FIG. 15B is a drawing explaining an example of arrangement of thesub-matrixes for forming a screen angle θ of 45°. As shown in FIG. 15B,by arranging the sub-matrixes 64 of 3×3 so as to be shifted by threeelements in the lateral direction and three elements in the verticaldirection, the basic unit for forming the screen angle of 45° isconfigured. By arranging the sub-matrixes of n×n by shifting in thelateral direction and the vertical direction by n elements respectively,the screen angle θ of 45° is achieved in the same manner.

FIG. 15C shows an example in which the inter-sub-matrix cell C whichcorresponds to two elements in the vertical direction is interposedbetween the sub-matrixes 60 of 4×4. With the arrangement of thesub-matrixes 60 as shown in FIG. 15C, the screen angle θ of about 27° isachieved.

As described with reference to FIGS. 14A, 14B and 14C and FIGS. 15A, 15Band 15C, by adjusting the size and arrangement of the sub-matrixes,adjustment of the screen angle θ and the number of screen lines todesired values is achieved.

FIG. 16A is a drawing showing a relationship between the basic units 62and the dither matrix 52 a configured as an assembly of the basic units62. Here, the number of elements in the dither matrix 52 a is equal tothe number of tones which is expressible within the range that thedither matrix 52 a covers. Therefore, the number of the basic units 62which constitute the dither matrix 52 a is calculated on the basis ofthe desired number of tones which are to be expressed by the dithermatrix 52 a and the number of elements in the basic unit 62. Forexample, when the number of tones to be expressed in the dither matrix52 a is 256 tones, and the number of elements in the single basic unit62 is sixty five, it is understood that the single dither matrix 52 acan be configured by four basic units 62 (that is, sixteen sub-matrixes60).

Subsequently, values from 1 to 16 are allocated as the smallestthreshold values to the respective sub-matrixes 60. FIG. 16B is adrawing showing an example of the smallest threshold values to beallocated to the respective sub-matrixes 60. The smallest thresholdvalues allocated here are provisional smallest threshold valuesallocated temporarily in order to allocate the threshold values of 256tones to the dither matrix 52 a uniformly.

Subsequently, as shown in FIG. 17, the size of a large dither 63configured of an assembly of the dither matrixes 52 a is determined.More specifically, spots where the same smallest threshold values aregenerated at the same position in the lateral direction and at the sameposition in the vertical direction are searched, and a size covering arange to the corresponding spots is determined as the size of the largedither 63. For example, as shown in FIG. 16, a spot X1 where thesmallest threshold value “1” is generated is determined as an apex, anda size defined by a spot X3 which is located at the same position in thevertical direction as the spot X1 and where the same smallest thresholdvalue “1” is generated and a spot X5 which is located at the sameposition in the lateral direction as the spot X1 and where the samesmallest threshold value “1” is generated is determined as the size ofthe large dither 63.

A procedure to calculate the distance from the spot X1 to the spot X3and the distance from the spot X1 to the spot X5 (that is, the size ofthe large dither 63) will be described below. First of all, a spot X2where the same smallest threshold value “1” as the spot X1 is generatedis searched. In the example shown in FIGS. 15A and 15B, the distancebetween the spot X1 and the spot X2 is apart from each other by anextent corresponding to sixteen threshold values in the verticaldirection and is apart from each other by an extent corresponding tofour threshold values in the lateral direction. Also, a range from thespot X2 to a spot X4 where the same smallest threshold value “1” isgenerated corresponds to sixteen threshold values in the lateraldirection and to four threshold values in the vertical direction.

Therefore, from an expression 16÷4=4, it is understood that four dithermatrixes 52 a can be arranged in a range from the spot X3 to the spotX2. Therefore, the number of threshold values to be arranged in thelateral direction from the spot X2 to the spot X3 is calculated as sixtyfour from an expression 16×4=64.

The spot X1 and the spot X2 are apart from each other in the lateraldirection by an extent corresponding to four threshold values.Therefore, from an expression 64+4=68, the number of the thresholdvalues included in a range from the spot X1 to the spot X3 (that is, thelateral size of the large dither 63) can be calculated as sixty eightthreshold values. In the same manner, the number of the threshold valuesincluded in a range from the spot X1 to the spot X5 (that is, thevertical size of the large dither) can be calculated.

The dither matrixes designed by the process described later are storedin the ROM 52 (see FIG. 3) in the unit of the large dither determined inthis manner.

Subsequently, the shape of the dots to be formed corresponding to therespective sub-matrixes 60 is selected. As the dot shape, there are“circle”, “oval”, “square”, and “diamond shape” in detail, and the dotshape which meets the application or the resolution may be selected.Here, description will be made assuming that the rod-like dot shapewhich is suitable for the laser printer 1 is selected.

FIG. 18A is a drawing showing an example of a sequence of growth of thedot for forming the rod-like dot parallel to the primary scanningdirection. As shown in FIG. 18A, the sub-matrixes 60 and theinter-sub-matrix cell C which assume the desired dot shape can bedesigned by designing the sub-matrixes 60 and the inter-sub-matrix cellC in such a manner that the larger the sequence of growth of the dot,the larger the threshold value to be allocated becomes, that is, byallocating the threshold values in an ascending order according to thesequence of growth of the dot.

As shown in FIG. 18A, when determining the sequence of growth of thedot, the dot formed corresponding to the sub-matrix 60 is formed intothe rod-like dot shape by extending from a position corresponding to theupper left corner of the sub-matrix 60 as an original point in theprimary scanning direction.

FIG. 18B is a drawing showing an example of the threshold valuesallocated to the dither matrix 52 a according to the smallest thresholdvalue shown in FIG. 16B and the sequence of growth of the dot shown inFIG. 18A. The smallest threshold value allocated as shown in FIG. 16B isarranged at the upper left corner of the sub-matrix 60, and thethreshold values are arranged by adding the smallest threshold value by“16” in the sequence of growth of the dot shown in FIG. 18A (see FIG.18B). Accordingly, the threshold values from 1 to 256 can be allocateddispersedly. Subsequently, the threshold values arranged in the dithermatrix 52 a in this manner are fine-adjusted.

FIGS. 19A and 19B are drawings explaining examples of adjustment of thethreshold values arranged in the dither matrix 52 a. For example, when afeature such that the toner can hardly be fixed is observed in the laserprinter 1, the pixels to be adhered with the toner can be increased byreducing the threshold values to be arranged in the dither matrix 52 a,so that the dots having an adequate size can be formed even when thetoner can hardly be fixed.

Therefore, as shown in FIG. 19A, the provisional smallest thresholdvalues “1, 2, 3, 4” allocated initially to the sub-matrixes are changedto “1” (sub-matrix 60A). In the same manner, the provisional smallestthreshold values “5, 6, 7, 8” allocated initially to the sub-matrixesare changed to “2” (sub-matrix 60B). In the same manner, the provisionalsmallest threshold values “9, 10, 11, 12, 13, 14, 15, 16” allocatedinitially to the sub-matrixes are changed to “3” (sub-matrix 60C).Subsequently, the threshold values from “4” to “19” as the secondsmallest threshold values from the smallest threshold values “1, 2, 3”after the change are allocated to immediate right of the smallestthreshold value respectively in any sub-matrix. Then, with reference tothe allocated threshold values from “4” to “19”, the remaining thresholdvalues in the respective sub-matrixes 60 are set to values with theincrement of 16, so that the threshold values in the sub-matrix 60 arereset.

As shown in FIG. 19A, when the threshold values in the respectivesub-matrixes 60 are changed, a largest value of the threshold value inthe dither matrix 52 a is smaller than 255. For example, in the case ofFIG. 19A, the largest threshold value is 243. In this case, the valuesof all the pixels within the range that the dither matrix covers areconverted into “1” which means that the toner is fixed at the time pointof the input value 243, so that the tone from the input value 243 to theinput value 255 cannot be expressed.

Therefore, as shown in FIG. 19B, the threshold values are adjusted sothat the largest value among all the threshold values in the dithermatrix 52 a becomes 255. More specifically, the calculation of“threshold value×255÷(the largest threshold value at the time point ofFIG. 19A)”, if for example, the largest threshold value at the timepoint of FIG. 19A is 243, the calculation of the “thresholdvalue×255÷243” is performed for all the threshold values so that thethreshold values to 255 are allocated evenly. Values after the decimalpoint of the result of calculation are rounded off.

In this manner, as a result of adjustment of the largest value of thethreshold values, for example, if any threshold value becomes zero, oran irregularity such that the threshold value next to the thresholdvalue 20 becomes 27 is generated, so that inconvenience such that asmooth tone expression cannot be achieved is resulted, an operator whois in charge of creating the dither matrix 52 a may return to any partof the procedure shown in FIGS. 14A, 14B, and 14C to FIGS. 19A and 19Band retry the operation again.

The created dither matrix 52 a is stored in the ROM 52 (see FIG. 3) inthe unit of the large dither 63 determined in FIG. 17. Accordingly, inthe halftoning, a range corresponding to a plurality of the dithermatrixes 52 a can be processed at once by superimposing the large dither63 on the input image and performing the comparison with the thresholdvalues.

The dither matrixes from Pattern 1 to Pattern 8 described with referenceto FIGS. 6A and 6B to FIG. 12 can be designed in the same procedure.

In this embodiment, description has been made assuming that the laserprinter 1 stores the dither matrixes 52 a, and the halftoning isperformed in the laser printer 1. In contrast, it is also possible toconfigure in such a manner that the halftoning is performed in theexternal data processing instrument such as the personal computer andthe image data is outputted into the laser printer.

FIG. 20 is a block diagram showing an electric configuration of apersonal computer 80 (hereinafter referred to as PC 80), and a laserprinter 90 connected to the PC 80 so as to allow the communicationtherewith. The laser printer 90 comprises a photoconductor drum, a laserscanner apparatus configured to scan the photoconductor drum in theprimary scanning direction according to the image data, a drum gearconfigured to transmit a drive force from the drive source to thephotoconductor drum, and a drum driving gear. The configurations of thephotoconductor drum, the laser scanner apparatus, the drum gear, and thedrum driving gear may be the same configuration as those of the laserprinter 1 described in the embodiment, detailed illustration anddescription are omitted.

The PC 80 comprises a CPU 81, a ROM 82, a RAM 83, an HDD (hard diskdrive) 84, and an interface 86 for connecting with the laser printer 90.

As shown in FIG. 20, the HDD 84 stores a printer driver 84 a and adither matrix 84 b used for the halftoning. The CPU 81 functions asimage data generating unit configured to generate image data byperforming the halftoning using the dither matrix 84 b according to theprinter driver 84 a.

The dither matrix 84 b is configured to include a plurality of thesub-matrixes having the threshold values set in such a manner that thedot grows into the rod-like shape from the original point in the primaryscanning direction as in the case of the dither matrix 52 a in theembodiment arranged regularly.

In this case as well, the generation of the inconsistencies in densityon the printing paper is restrained by configuring in such a manner thatthe gear pitch a determined on the basis of the configuration of thelaser printer 90 and the line pitch b determined on the basis of thedither matrix stored in the PC 80 satisfy the relational expression;a≧0.24 mm and b/a<0.78, or a<0.24 mm and b/a>1.2, in the same manner asthe laser printer 1 in the embodiment.

Although the number of colors used in the laser printer 1 is assumed tobe one in the description in the embodiment described above, a colorlaser printer which forms images with toner in a plurality of colors maybe applicable. When the image is formed with the toner in the pluralityof colors, the dither matrixes to be applied are differentiated on thecolor-to-color basis, and the screen angles are differentiated on thecolor-to-color basis. In this case as well, the generation of theinconsistencies in density on the printing paper may be reduced orrestrained by configuring in such a manner that the line pitch b and thegear pitch a determined from the dither matrixes in respective colorsrespectively satisfy the relational expression; a≧0.24 mm and b/a<0.78,or a<0.24 mm and b/a>1.2, in the same manner as the laser printer 1 inthe embodiment.

While the invention has been described in connection with embodiments,it will be understood by those skilled in the art that other variationsand modifications of the embodiments described above may be made withoutdeparting from the scope of the invention. Other embodiments will beapparent to those skilled in the art from a consideration of thespecification or practice of the invention disclosed herein. It isintended that the specification and the described examples areconsidered merely as exemplary of the invention, with the true scope ofthe invention being indicated by the flowing claims.

1. An image forming apparatus comprising: an image data generating unitconfigured to convert a tone of an input value which indicates a densityof a pixel by using a predetermined dither matrix and generate imagedata; a scanning unit configured to scan an image carrier in a primaryscanning direction according to the image data generated by the imagedata generating unit; an image forming unit configured to form, on aprinting medium, an image corresponding to the image data scanned by thescanning unit; a drive source; and a gear configured to transmit a driveforce from the drive source to the image carrier, wherein the dithermatrix includes a plurality of sub-matrixes arranged in a predeterminedrule and each of the plurality of sub-matrix having predeterminedthreshold values such that a dot in each of the plurality of thesub-matrixes grows from a corresponding original point, the plurality ofsub-matrixes includes a first sub-matrix and a second sub-matrix whichhas a predetermined positional relation with the first sub-matrix,wherein the image forming apparatus satisfies a relation ofa≧0.24 mm and b/a<0.78, or  (1)a<0.24 mm and b/a>1.2  (2) where “a” is a travel distance of a printingmedium per tooth of the gear in a secondary scanning directionorthogonal to the primary scanning direction, and “b” is a component inthe secondary scanning direction of a distance between the originalpoint of the dot derived from the first sub-matrix and the originalpoint of the dot derived from the second sub-matrix.
 2. The imageforming apparatus according to claim 1, wherein the second sub-matrix isone of the sub-matrixes next to the first sub-matrix and is positionedsuch that the distance b is larger than the others of the sub-matrixesnext to the first sub-matrix.
 3. The image forming apparatus accordingto claim 1, wherein the image forming apparatus satisfies the relationof (1) a≧0.24 mm and b/a<0.78.
 4. The image forming apparatus accordingto claim 1, wherein the image forming apparatus satisfies the relationof (2) a<0.24 mm and b/a>1.2.
 5. An image forming system comprising: animage forming apparatus comprising: a scanning unit configured to scanan image carrier in a primary scanning direction according to imagedata; an image forming unit configured to form, on a printing medium, animage corresponding to the image data scanned by the scanning unit; adrive source; and a gear configured to transmit a drive force from thedrive source to the image carrier; and a computer which communicate withthe image forming apparatus, the computer comprises an image datagenerating unit configured to convert an input value which indicates adensity of a pixel by using a predetermined dither matrix and generateimage data, the dither matrix includes a plurality of sub-matrixesarranged in a predetermined rule, each of the plurality of sub-matrixhaving predetermined threshold values such that a dot in each of theplurality of the sub-matrixes grows from a corresponding original point,the plurality of sub-matrixes includes a first sub-matrix and a secondsub-matrix which has a predetermined positional relation with the firstsub-matrix, wherein the image forming apparatus satisfies a relation ofa≧0.24 mm and b/a<0.78, or  (1)a<0.24 mm and b/a>1.2  (2) where “a” is a travel distance of a printingmedium per tooth of the gear in a secondary scanning directionorthogonal to the primary scanning direction, and “b” is a component inthe secondary scanning direction of a distance between the originalpoint of the dot derived from the first sub-matrix and the originalpoint of the dot derived from the second sub-matrix.
 6. The imageforming system according to claim 5, wherein the second sub-matrix isone of the sub-matrixes next to the first sub-matrix and is positionedsuch that the distance b is larger than the others of the sub-matrixesnext to the first sub-matrix.
 7. The image forming system according toclaim 5, wherein the image forming system satisfies the relation of (1)a≧0.24 mm and b/a<0.78.
 8. The image forming system according to claim5, wherein the image forming system satisfies the relation of (2) a<0.24mm and b/a>1.2.